Complementarities between mathematical and computational modeling: the case of the repeated Prisoners' Dilemma

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the mathematical model. Our main conclusion is that mathematical and computational models are good complements for research in social sciences. Indeed, while computational models are extremely useful to extend the scope of the analysis to complex scenarios hard to analyze mathematically, formal models can be useful to verify and to explain the outcomes of computational models.

Univariate versus multivariate modeling of panel data

Panel data can be arranged into a matrix in two ways, called 'long' and 'wide' formats (LFand WF). The two formats suggest two alternative model approaches for analyzing paneldata: (i) univariate regression with varying intercept; and (ii) multivariate regression withlatent variables (a particular case of structural equation model, SEM). The present papercompares the two approaches showing in which circumstances they yield equivalent?insome cases, even numerically equal?results. We show that the univariate approach givesresults equivalent to the multivariate approach when restrictions of time invariance (inthe paper, the TI assumption) are imposed on the parameters of the multivariate model.It is shown that the restrictions implicit in the univariate approach can be assessed bychi-square difference testing of two nested multivariate models. In addition, commontests encountered in the econometric analysis of panel data, such as the Hausman test, areshown to have an equivalent representation as chi-square difference tests. Commonalitiesand differences between the univariate and multivariate approaches are illustrated usingan empirical panel data set of firms' profitability as well as a simulated panel data.

A mathematical excursion: From the three-door problem to a Cantor-type perfect set

We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.

On the impact of fundamentals, liquidity and coordination on market stability

We develop a coordination game to model interactions betweenfundamentals and liquidity during unstable periods in financial markets.We then propose a flexible econometric framework for estimationof the model and analysis of its quantitative implications. The specificempirical application is carry trades in the yen dollar market, includingthe turmoil of 1998. We find a generally very deep market, withlow information disparities amongst agents. We observe occasionallyepisodes of market fragility, or turmoil with up by the escalator, downby the elevator patterns in prices. The key role of strategic behaviorin the econometric model is also confirmed.

Exact and approximate stepdown methods for multiple hypothesis testing

Consider the problem of testing k hypotheses simultaneously. In this paper,we discuss finite and large sample theory of stepdown methods that providecontrol of the familywise error rate (FWE). In order to improve upon theBonferroni method or Holm's (1979) stepdown method, Westfall and Young(1993) make eective use of resampling to construct stepdown methods thatimplicitly estimate the dependence structure of the test statistics. However,their methods depend on an assumption called subset pivotality. The goalof this paper is to construct general stepdown methods that do not requiresuch an assumption. In order to accomplish this, we take a close look atwhat makes stepdown procedures work, and a key component is a monotonicityrequirement of critical values. By imposing such monotonicity on estimatedcritical values (which is not an assumption on the model but an assumptionon the method), it is demonstrated that the problem of constructing a validmultiple test procedure which controls the FWE can be reduced to the problemof contructing a single test which controls the usual probability of a Type 1error. This reduction allows us to draw upon an enormous resamplingliterature as a general means of test contruction.

Simple and fast methods based on solid-phase extraction coupled to liquid chromatography with UV detection for the monitoring of caffeine in natural and waste waters as marker of anthropogenic impact

Two concentration methods for fast and routine determination of caffeine (using HPLC-UV detection) in surface, and wastewater are evaluated. Both methods are based on solid-phase extraction (SPE) concentration with octadecyl silica sorbents. A common “offline” SPE procedure shows that quantitative recovery of caffeine is obtained with 2 mL of an elution mixture solvent methanol-water containing at least 60% methanol. The method detection limit is 0.1 μg L−1 when percolating 1 L samples through the cartridge. The development of an “online” SPE method based on a mini-SPE column, containing 100 mg of the same sorbent, directly connected to the HPLC system allows the method detection limit to be decreased to 10 ng L−1 with a sample volume of 100 mL. The “offline” SPE method is applied to the analysis of caffeine in wastewater samples, whereas the “on-line” method is used for analysis in natural waters from streams receiving significant water intakes from local wastewater treatment plants

A limited area model intercomparison on the "Montserrat-2000" flash-flood event using statistical and deterministic methods

In the scope of the European project Hydroptimet, INTERREG IIIB-MEDOCC programme, limited area model (LAM) intercomparison of intense events that produced many damages to people and territory is performed. As the comparison is limited to single case studies, the work is not meant to provide a measure of the different models' skill, but to identify the key model factors useful to give a good forecast on such a kind of meteorological phenomena. This work focuses on the Spanish flash-flood event, also known as "Montserrat-2000" event. The study is performed using forecast data from seven operational LAMs, placed at partners' disposal via the Hydroptimet ftp site, and observed data from Catalonia rain gauge network. To improve the event analysis, satellite rainfall estimates have been also considered. For statistical evaluation of quantitative precipitation forecasts (QPFs), several non-parametric skill scores based on contingency tables have been used. Furthermore, for each model run it has been possible to identify Catalonia regions affected by misses and false alarms using contingency table elements. Moreover, the standard "eyeball" analysis of forecast and observed precipitation fields has been supported by the use of a state-of-the-art diagnostic method, the contiguous rain area (CRA) analysis. This method allows to quantify the spatial shift forecast error and to identify the error sources that affected each model forecasts. High-resolution modelling and domain size seem to have a key role for providing a skillful forecast. Further work is needed to support this statement, including verification using a wider observational data set.

The European Union in North Korea: Current Realities and Paths for Future Engagement – A Qualitative and Quantitative Study

Malgrat la rellevància estratègica i el paper desestabilitzador de Corea del Nord a la regió econòmicament més dinàmica del món, la UE no compta amb cap estratègia clara per involucrar-se amb aquest país. Combinant tècniques d’anàlisi qualitatives i quantitatives, aquest treball pretén descobrir possibles contradiccions internes que impedeixin la definició d'una política exterior europea coherent i efectiva amb respecte a Corea del Nord, així com discrepàncies entre les percepcions d’actors interns de la UE i les d’actors externs. S'han detectat importants diferències d’expectatives i mancances en termes de coherència, tant entre les visions expressades pels actors interns com entre les opinions d’aquests actors i les dels futurs líders sudcoreans enquestats – diferències que fins i tot afecten la promoció dels drets humans

The illusion of control, the structures of prizes and the demand for football pools in Spain

Using data for all the fixtures for the seasons from 1972-73 to 2002-03, we estimate a dynamic model of demand for football pools in Spain paying attention to whether their main economic explanatory variable is the effective price of a ticket or the jackpot. Additionally, we evaluate the importance of the composition of the list of games in terms of whether First Division matches are included or not. Results show that the jackpot model is preferred to the effective price model, having important implications in terms of how the structure of the game should be changed in order to increase demand.

Resolució de problemes i mètode de raonament en l'educació matemàtica

Des del principi dels temps històrics, la Matemàtica s'ha generat en totes les civilitzacions sobre la base de la resolució de problemes pràctics.Tanmateix, a partir del període grec la Història ens mostra la necessitat de fer un pas més endavant: l'evolució històrica de la Matemàtica situa els mètodes de raonament com a eix central de la recerca en Matemàtica. A partir d'una ullada als objectius i mètodes de treball d'alguns autors cabdals en la Història dels conceptes matemàtics postulem l'aprenentatge de les formes de raonament matemàtic com l'objectiu central de l'educació matemàtica, i la resolució de problemes com el mitjà més eficient per a coronar aquest objectiu.English version.From the beginning of the historical times, mathematics has been generated in all the civilizations on the base of the resolution of practical problems. Nevertheless, from the greek period History shows us the necessity to take one more step: the historical evolution of mathematics locates the methods of reasoning as the central axis of the research in mathematics. Glancing over the objectives and methods of work used bysome fundamental authors in the History of the mathematical concepts we postulated the learning of the forms of mathematical reasoning like the central objective of the mathematical education, and the resolution of problems as the most efficient way to carry out this objective.

Strategies for sequential prediction of stationary time series

We present simple procedures for the prediction of a real valued sequence. The algorithms are based on a combinationof several simple predictors. We show that if the sequence is a realization of a bounded stationary and ergodic random process then the average of squared errors converges, almost surely, to that of the optimum, given by the Bayes predictor. We offer an analog result for the prediction of stationary gaussian processes.

Stepwise multiple testing as formalized data snooping

It is common in econometric applications that several hypothesis tests arecarried out at the same time. The problem then becomes how to decide whichhypotheses to reject, accounting for the multitude of tests. In this paper,we suggest a stepwise multiple testing procedure which asymptoticallycontrols the familywise error rate at a desired level. Compared to relatedsingle-step methods, our procedure is more powerful in the sense that itoften will reject more false hypotheses. In addition, we advocate the useof studentization when it is feasible. Unlike some stepwise methods, ourmethod implicitly captures the joint dependence structure of the teststatistics, which results in increased ability to detect alternativehypotheses. We prove our method asymptotically controls the familywise errorrate under minimal assumptions. We present our methodology in the context ofcomparing several strategies to a common benchmark and deciding whichstrategies actually beat the benchmark. However, our ideas can easily beextended and/or modied to other contexts, such as making inference for theindividual regression coecients in a multiple regression framework. Somesimulation studies show the improvements of our methods over previous proposals. We also provide an application to a set of real data.

Modelos estadísticos y evaluación: tres estudios en educación

The educational system in Spain is undergoing a reorganization. At present, high-school graduates who want to enroll at a public university must take a set of examinations Pruebas de Aptitud para el Acceso a la Universidad (PAAU). A "new formula" (components, weights, type of exam,...) for university admission is been discussed. The present paper summarizes part of the research done by the author in her PhD. The context for this thesis is the evaluation of large-scale and complex systems of assessment. The main objectives were: to achieve a deep knowledge of the entire university admissions process in Spain, to discover the main sources of uncertainty and topromote empirical research in a continual improvement of the entire process. Focusing in the suitable statistical models and strategies which allow to high-light the imperfections of the system and reduce them, the paper develops, among other approaches, some applications of multilevel modeling.

Optimised search heuristic combining valid inequalities and tabu search

This paper presents an Optimised Search Heuristic that combines a tabu search method with the verification of violated valid inequalities. The solution delivered by the tabu search is partially destroyed by a randomised greedy procedure, and then the valid inequalities are used to guide the reconstruction of a complete solution. An application of the new method to the Job-Shop Scheduling problem is presented.

Ratio maps and correspondence analysis

We compare two methods for visualising contingency tables and developa method called the ratio map which combines the good properties of both.The first is a biplot based on the logratio approach to compositional dataanalysis. This approach is founded on the principle of subcompositionalcoherence, which assures that results are invariant to considering subsetsof the composition. The second approach, correspondence analysis, isbased on the chi-square approach to contingency table analysis. Acornerstone of correspondence analysis is the principle of distributionalequivalence, which assures invariance in the results when rows or columnswith identical conditional proportions are merged. Both methods may bedescribed as singular value decompositions of appropriately transformedmatrices. Correspondence analysis includes a weighting of the rows andcolumns proportional to the margins of the table. If this idea of row andcolumn weights is introduced into the logratio biplot, we obtain a methodwhich obeys both principles of subcompositional coherence and distributionalequivalence.